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(a) What is the 2 x 2 matrix M that reflects v = ( 7 ) to ( ² ) ? y for M-1 makes sense geometrically. (+) across the x axis, i.e. takes ? Find the inverse matrix of M and explain why your answer (V³). (3) across the line l, by using matrix multiplication to compose M from part (a) with a rotation by an appropriate angle 0. Find the 2x2 matrix N that reflects v = (b) Let & be the line through the origin (0,0) that is parallel to the vector (c) Find N-1 in two ways: by applying the usual formula for the inverse of a 2 × 2 matrix to N, and by using the rule (AB)-¹ = B-¹A-¹ and your representation of N as a product from part (b).

(a) What is the 2 x 2 matrix M that reflects v = ( 7 ) to ( ² ) ? y for M-1 makes sense geometrically. (+) across the x axis, i.e. takes ? Find the inverse matrix of M and explain why your answer (V³). (3) across the line l, by using matrix multiplication to compose M from part (a) with a rotation by an appropriate angle 0. Find the 2x2 matrix N that reflects v = (b) Let & be the line through the origin (0,0) that is parallel to the vector (c) Find N-1 in two ways: by applying the usual formula for the inverse of a 2 × 2 matrix to N, and by using the rule (AB)-¹ = B-¹A-¹ and your representation of N as a product from part (b).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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2. (a) What is the 2 x 2 matrix M that reflects v = = ($) across the x axis, i.e. takes ? Find the inverse matrix of M and explain why your answer X (") to ( ²₁ ) ? Y for M-1 makes sense geometrically. (V³). - (+) across the line l, by using matrix multiplication to compose M from part (a) with a rotation by an appropriate angle 0. (b) Let & be the line through the origin (0, 0) that is parallel to the vector Find the 2x2 matrix N that reflects v = (c) Find N-1 in two ways: by applying the usual formula for the inverse of a 2 x 2 matrix to N, and by using the rule (AB)-¹ = B-¹A-¹ and your representation of N as a product from part (b).
Transcribed Image Text:2. (a) What is the 2 x 2 matrix M that reflects v = = ($) across the x axis, i.e. takes ? Find the inverse matrix of M and explain why your answer X (") to ( ²₁ ) ? Y for M-1 makes sense geometrically. (V³). - (+) across the line l, by using matrix multiplication to compose M from part (a) with a rotation by an appropriate angle 0. (b) Let & be the line through the origin (0, 0) that is parallel to the vector Find the 2x2 matrix N that reflects v = (c) Find N-1 in two ways: by applying the usual formula for the inverse of a 2 x 2 matrix to N, and by using the rule (AB)-¹ = B-¹A-¹ and your representation of N as a product from part (b).
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